Exercise 26 Page 228

To solve the given problem we will form two equations and combine them into a system. We are told that the investor owns a total of 200 shares. If we let x represents the number of shares of Stock A and y represents the number of shares of Stock B, we can write the first equation. x+y=200 Using the given stock prices we can write the total value of shares in terms of x and y. However, we also know that the total value of investor's shares equals $4000. Let's equate these terms to obtain the second equation. 9.5x+27y=4000 Since variable y in the first equation can be isolated in just one step, we will use the Substitution Method.

x+y=200 & (I) 9.5x+27y=4000 & (II)

SubEqn

(I):LHS-x=RHS-x

y=200-x 9.5x+27y=4000

Substitute

(II):y= 200-x

y=200-x 9.5x+27( 200-x)=4000

Distr

(II):Distribute 27

y=200-x 9.5x+5400-27x=4000

SubEqn

(II):LHS-5400=RHS-5400

y=200-x 9.5x-27x=-1400

SubTerm

(II):Subtract term

y=200-x -17.5x=-1400

DivEqn

(II):.LHS /-17.5.=.RHS /-17.5.

y=200-x x=80

Now, to find the value of y we need to substitute x=8 into either one of the equations in the given system. Let's use the first equation.

y=200-x x=80

Substitute

(I):x= 80

y=200- 80 x=80

SubTerm

Subtract term

y=120 x=80

The solution to the system of equation is x=80 and y=120. This means that the investor owns 80 shares of Stock A and 120 shares of Stock B.